Finite Group Databasebeta

← #14658567

Subgroups — #14658567

Order 2816.

310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069436C211yesmaximal, characteristic
2#13067289C212yesmaximal
3#13066476C212yesmaximal
4#13066461C211yesmaximal, characteristic
5C11×#1849C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C2×C11×#108—21no—
8C2×C11×#108—21no—
9C11×#423C2212yes—
10C2×C11×#97C2211yescharacteristic
11C2×#66880—21no—
12C2×#66880—21no—
13#10622549C2211yescharacteristic
14#10622538C2212yes—
15#10622120—24no—
16C22×Dic22—21no—
17C2×C11×M16—22no—
18C22×C8×C11D411yescharacteristic
19C22×C8×C11D411yescharacteristic
20C2×C42×C11C2311yescharacteristic
21C2×C4⋊Dic11—22no—
22C2×C4⋊Dic11—21no—
23#66922—22no—
24#66922—21no—
25#66922D412yes—
26C11×#108—42no—
27C11×#108—42no—
28C11×C4⋊C8—22no—
29C11×C4⋊C8—22no—
30C11×#97—22no—
31C11⋊#95—22no—
32C22⋊(C11⋊C8)—22no—
33#66880—42no—
34#66880—42no—
35C4⋊(C11⋊C8)—22no—
36C4×C11⋊C8—22no—
37#10632—111nomaximal, Sylow
38C22×C4×C11C2×D411yescharacteristic
39C22×C4×C11#4112yes—
40C22×Dic11—41no—
41C22×Dic11—41no—
42C2×Dic22—22no—
43C2×Dic22—41no—
44C2×Dic22—41no—
45C2×Dic22—41no—
46C2×Dic22—41no—
47C2×Dic22—41no—
48C11×M16—42no—
49C11×M16—42no—
50C2×C8×C11—21no—
51C2×C8×C11—21no—
52C2×C8×C11—21no—
53C2×C8×C11—21no—
54C2×C8×C11—42no—
55C2×C8×C11D812yes—
56C2×C8×C11SD1612yes—
57C42×C11C2×D411yescharacteristic
58C42×C11#4111yescharacteristic
59C42×C11#4112yes—
60C4⋊Dic11—24no—
61C4⋊Dic11—42no—
62C4⋊Dic11—41no—
63C4⋊Dic11—41no—
64C2×C11⋊C8—42no—
65#1960—111no—
66#1849D1111yescharacteristic
67#1546—112no—
68#1286—112no—
69#1281—111no—
70C23×C11#12411yescharacteristic
71C2×C4×C11—42no—
72C2×C4×C11#12111yescharacteristic
73C2×C4×C11#12312yes—
74C2×C4×C11#12311yescharacteristic
75C2×C4×C11#12612yes—
76C2×C4×C11C2×D811yescharacteristic
77C2×C4×C11C2×SD1611yescharacteristic
78C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
79C2×C4×C11#13711yescharacteristic
80C2×Dic11—42no—
81C2×Dic11—81no—
82C2×Dic11—81no—
83C2×Dic11—82no—
84C2×Dic11—81no—
85Dic22—42no—
86Dic22—42no—
87Dic22—81no—
88Dic22—81no—
89C8×C11—22no—
90C8×C11—22no—
91C8×C11—82no—
92C11⋊C8—82no—
93C2×C4⋊Q8—111no—
94#431—112no—
95C2×#108—21no—
96C2×#108—21no—
97#423C2×D1112yes—
98C2×#103—221no—
99C2×#103—221no—
100C2×#97C2×D1111yescharacteristic
101#382—111no—
102#332—224no—
103C22×C11—22no—
104C22×C11#39711yescharacteristic
105C22×C11#48611yescharacteristic
106C22×C11#48911yescharacteristic
107C4×C11—22no—
108C4×C11—22no—
109C4×C11#45911yescharacteristic
110C4×C11#46111yescharacteristic
111C4×C11#48011yescharacteristic
112C4×C11#48111yescharacteristic
113Dic11—82no—
114Dic11—161no—
115C22×Q8—221no—
116C2×M16—22no—
117C22×C8C22⋊D1111yescharacteristic
118C22×C8C22⋊D1111yescharacteristic
119C4⋊Q8—112no—
120C4⋊Q8—222no—
121C4⋊Q8—221no—
122C2×C4⋊C4—222no—
123C2×C4⋊C4—221no—
124C2×C42C22×D1111yescharacteristic
125#108—42no—
126#108—42no—
127C4⋊C8—22no—
128C4⋊C8—22no—
129C4⋊C8—222no—
130#103—442no—
131#103—442no—
132C22⋊C8—222no—
133#97—22no—
134C4×C8—222no—
135#95—222no—
136C2×C11—21no—
137C2×C11—21no—
138C2×C11#207111yescharacteristic
139C2×C11#208212yes—
140C2×Q8—222no—
141C2×Q8—441no—
142C2×Q8—441no—
143C2×Q8—441no—
144C2×Q8—441no—
145C2×Q8—441no—
146C22×C4—441no—
147C22×C4—441no—
148C22×C4#434312yes—
149C22×C4C2×C22⋊D1111yescharacteristic
150M16—42no—
151M16—42no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—42no—
157C2×C8—442no—
158C2×C8#432312yes—
159C2×C8#432512yes—
160C4⋊C4—224no—
161C4⋊C4—442no—
162C4⋊C4—441no—
163C4⋊C4—441no—
164C42#433912yes—
165C42D4×D1111yescharacteristic
166C42#434111yescharacteristic
167C11#1063211yescharacteristic, complemented, Sylow
168C23#6700011yescharacteristic
169Q8—442no—
170Q8—442no—
171Q8—881no—
172Q8—881no—
173C2×C4—42no—
174C2×C4—442no—
175C2×C4—881no—
176C2×C4—881no—
177C2×C4—882no—
178C2×C4—881no—
179C2×C4#6694712yes—
180C2×C4#6695112yes—
181C2×C4#6698211yescharacteristic
182C2×C4C2×#432311yescharacteristic
183C2×C4#6698511yescharacteristic
184C2×C4#6699111yescharacteristic
185C2×C4C2×#432511yescharacteristic
186C2×C4#6699511yescharacteristic
187C8—22no—
188C8—22no—
189C8—82no—
190C8—882no—
191C22—22no—
192C22#1062260611yescharacteristic
193C22#1062270111yescharacteristic
194C22#1062270211yescharacteristic
195C4—22no—
196C4—22no—
197C4—882no—
198C4—1761no—
199C4#1062258011yescharacteristic
200C4#1062258111yescharacteristic
201C4#1062268511yescharacteristic
202C4#1062269611yescharacteristic
203C2—21no—
204C2—21no—
205C2#1307002011yescharacteristic
206C2#1307008112yes—
subgroupG/H
centerC22#10622606
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1849C2
socleC22×C11#397
prime radicalC23×C11#124
hypercenter#1849D11
hypocenterC11#10632
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1849

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
167. C11#10632semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130694362
#130672892
#130664762
#130664612
C11×#18492
#1063211